GPS_Erros and Biases

1. Maneeb Masood
15152010
Errors and Biases in
GPS

2. Introduction
 GPS range and carrier-phase measurements are
both affected by several types of random errors and
biases (systematic errors).
Errors arise from a variety of sources.
 Satellite positions (geometry)
 Weather
 Multipath
 Timing errors
 These errors are broadly classified into;
(a) those originating at the satellites:
ephemeris, or orbital, errors, satellite clock errors,
and the effect of selective availability.
(b) those originating at the receiver:
receiver clock errors, multipath error, receiver noise,
and antenna phase center variations.

3.  (c) those that are due to signal propagation
(atmospheric refraction)
delays of the GPS signal as it passes through the
ionospheric and tropospheric layers of the
atmosphere
 In addition to these, the accuracy of the GPS
position is also affected by the geometric locations
of the GPS satellites as seen by the receiver.
 In fact, it is only in a vacuum (free space) that the
GPS signal travels, or propagates, at the speed of
light.
 Typical error is 10+ meters.
 All GPS are 12 channel: can receive up to 12
satellites

4. GPS Ephemeris Errors
 Modeling the forces acting on the GPS satellites will
not in general be perfect, which causes some errors in
the estimated satellite positions, known as ephemeris
errors.
 Forces on the GPS satellite
 Earth is not a perfect sphere and hence uneven
gravitational potential distribution
 Other heavenly bodies attract the satellite, but these are
very well modeled
 Not a perfect vacuum hence drag but it is negligible at
GPS orbits
 Solar radiation effects which depends on the surface
reflectivity, luminosity of the sun distance of to the sun.
This error is the largest unknown errors source.

5. Selective Availability
 To ensure national security, the U.S. DoD
implemented the so-called selective availability
(SA) on Block II GPS satellites to deny accurate
real-time autonomous positioning to unauthorized
users. SA was officially activated on March 25,
1990
 SA introduces two types of errors.
(1) delta error, results from dithering the satellite
clock, and is common to all users worldwide.
(2) epsilon error, is an additional slowly varying
orbital error.

6. How the horizontal position of a stationary
GPS receiver varies over time, mainly as a
result of the effect of SA.

7.  The range error due to epsilon error is almost
identical between users of short separations.
Therefore, using differential GPS (DGPS) would
overcome the effect of the epsilon error. In fact,
DGPS provides better accuracy than the
standalone P-code receiver due to the elimination
or the reduction of the common errors, including
SA
 The U.S. government discontinued SA on May 1,
2000, resulting in a much-improved autonomous
GPS accuracy. With the SA turned off, the nominal
autonomous GPS horizontal and vertical
accuracies would be in the order of 22m and 33m.

9. Satellite and Receiver Clock
Errors
 Each GPS Block II and Block IIA satellite contains
four atomic clocks, two cesium and two rubidium.
The newer generation Block IIR satellites carry
rubidium clocks only. One of the onboard clocks,
primarily a cesium for Block II and IIA, is selected
to provide the frequency and the timing
requirements for generating the GPS signals. The
others are backups.
 The GPS satellite clocks, although highly
accurate, are not perfect.

10.  Satellite clock error is about 8.64 to 17.28 ns per
day. The corresponding range error is 2.59m to
5.18m, which can be easily calculated by
multiplying the clock error by the speed of light.
(One nanosecond error is equivalent to a range error
of about 30 cm)
 Satellite clock errors cause additional errors to
the GPS measurements. These errors are
common to all users observing the same satellite
and can be removed through differencing
between the receivers. Applying the satellite clock
correction in the navigation message can also
correct the satellite clock errors.

11.  GPS receivers, in contrast, use inexpensive
crystal clocks, which are much less accurate
than the satellite clocks. As such, the receiver
clock error is much larger than that of the GPS
satellite clock. It can, however, be removed
through differencing between the satellites or it
can be treated as an additional unknown
parameter in the estimation process.
 Precise external clocks (usually cesium or
rubidium) are used in some applications instead
of the internal receiver clock.
 Although the external atomic clocks have
superior performance compared with the internal
receiver clocks, they cost between a few
thousand dollars for the rubidium clocks to about

12. Multipath Error
• A signal that bounces of a smooth object and
hits the receiver antenna.
• Increases the length of time for a signal to
reach the receiver.
• A big position error results.
• Gravel roads
• Open water
• Snow fields
• Rock walls
• Buidlings

13.  Technically speaking, multipath error occurs when
the GPS signal arrives at the receiver antenna
through different paths. These paths can be the
direct line of sight signal and reflected signals
from objects surrounding the receiver antenna.
 Multipath distorts the original signal through
interference with the reflected signals at the GPS
antenna.
 Multipath-mitigation techniques, multipath error
is reduced to several meters, even in a highly
reflective environment

15.  There are several options to reduce the effect of
multipath. The straightforward option is to select
an observation site with no reflecting objects in
the vicinity of the receiver antenna.
 Another option to reduce the effect of multipath is
to use a chock ring antenna (a chock ring device
is a ground plane that has several concentric
metal hoops, which reduce the reflected signals).

16. Antenna-phase-center Variation
 GPS antenna receives the incoming satellite signal
and then converts its energy into an electric
current, which can be handled by the GPS
receiver.
 The point at which the GPS signal is received is
called the antenna phase center.
 Generally, the antenna phase center does not
coincide with the physical (geometrical) center of
the antenna. It varies depending on the elevation
and the azimuth of the GPS satellite as well as the
intensity of the observed signal. As a result,
additional range error can be expected.

17.  The size of the error caused by the antenna-
phase-center variation depends on the antenna
type, and is typically in the order of a few
centimeters.
 It is, however, difficult to model the antenna-
phase-center variation and, therefore, care has
to be taken when selecting the antenna type.
 Mixing different types of antennas or using
different orientations will not cancel the error.
Due to its rather small size, this error is neglecte
in most of the practical GPS applications.

18. Receiver Measurement Noise
 The receiver measurement noise results from the
limitations of the receiver’s electronics.
A good GPS system should have a minimum
noise level.
 The contribution of the receiver measurement
noise to the range error will depend very
much on the quality of the GPS receiver.
 Typical average value for range error due to
the receiver measurement noise is of the
order of 0.6m

19. Ionospheric Delay
 The ionosphere, which is a zone of charged
particles approximately 50-3000 kilometres
above the earth, causes signal delays which
vary from day to night and by solar activity.
 The altitude and thickness of thelayers vary with
time, as a result of the changes in the sun’s
radiation and the Earth’s magnetic field.
 Generally, ionospheric delay is of the order of
5m to 15m, but can reach over 150m under
extreme solar activities, at midday, and near the
horizon.

20.  The ionosphere is a dispersive medium, which
means it bends the GPS radio signal and changes
its speed as it passes through the various
Ionospheric layers to reach a GPS receiver.
Bending the GPS signal path causes a negligible
error, particularly if the satellite elevation angle is
greater than 5°.
 It is the change in the propagation speed that
causes a significant range error.
 As the ionosphere is a dispersive medium, it
causes a delay that is frequency dependent. The
lower the frequency, the greater the delay.

21.  The ionospheric delay is proportional to the number
of free electrons along the GPS signal path, called
the total electron content (TEC). TEC, however,
depends on a number of factors:
(1) the time of day (electron density level reaches a
daily maximum in early afternoon and a minimum
around midnight at local time);
(2) the time of year (electron density levels are
higher in winter than in summer);
(3) the 11-year solar cycle (electron density levels
reach a maximum value approx. every 11 years.
(4) the geographic location (electron density levels
are minimum in mid latitude regions and highly
irregular in polar, auroral, and equatorial regions).

22. Tropospheric Delay
 Tropospheric delays are primarily a factor of
atmospheric pressure ,temperature and
humidity.
 The troposphere is the electrically neutral
atmospheric region that extends up to about 50
km from the surface of the earth. The
troposphere is a non- dispersive medium for
radio frequencies below 15 GHz.
 As a result, it delays the GPS carriers and
codes identically. That is, the measured
satellite-to-receiver range will be longer than the
actual geometric range, which means that a
distance between two receivers will be longer

23.  Most receivers employ algorithms which reduce
the tropospheric errors to less than 3 metres.
Tropospheric delay may be broken into two
components, dry and wet.
 Dry component represents about 90% of the
delay and can be predicted to a high degree of
accuracy using mathematical models.
 Wet component depends on the water vapor
along the GPS signal path and is difficult to
measure.
 The tropospheric delay is frequency independent

24. Satellite Geometry Measures
 The overall positioning accuracy of GPS is
measured by the combined effect of the
unmodeled measurement errors and the effect of
the satellite geometry.
 In general, the more spread out the satellites are
in the sky the better the satellite geometry, and
vice versa.

25. (a) Good satellite geometry (b) bad
satellite geometry
[assuming a two-dimensional (2-D) case]

26. Ideal Satellite Geometry

27. Poor Satellite Geometry

28. Dilution of Precision (DOP)
 The satellite geometry effect can be measured by
a single dimensionless number called the dilution
of precision (DOP). The lower the value of the
DOP number, the better the geometric strength,
and vice versa.
 Dilution of Precision (DOP) reflects each
satellite’s position relative to the other
satellites being accessed by a receiver.
 DOP number is computed based on the relative
receiver-satellite geometry at any instance, that
is, it requires the availability of both the receiver
and the satellite coordinates. Approximate values
for the coordinates are generally sufficient
though, which means that the DOP value can be

29.  As a result of the relative motion of the satellites
and the receiver(s), the value of the DOP will
change over time. The changes in the DOP value,
however, will generally be slow except in the
following two cases: (1) a satellite is rising or
falling as seen by the user's receiver, and (2)
there is an obstruction between the receiver and
the satellite (e.g., when passing under a bridge)

30. Position Dilution of Precision
(PDOP)
 PDOP represents the contribution of satellite
geometry to the 3-D positioning accuracy.
 PDOP can be broken into two components:
horizontal dilution of precision (HDOP) and
vertical dilution of precision (VDOP).
 The former represents the satellite geometry
effect on the horizontal component of the
positioning accuracy, while the latter represents
the satellite geometry effect on the vertical
component of the positioning accuracy.

31. Thank you.